JPH0734201B2 - Polyhedral shape input display device - Google Patents

Description

DETAILED DESCRIPTION OF THE INVENTION [Industrial field of application] The present invention defines a polyhedral shape in a computer and observes and examines its external shape from various angles, for example, in the field of architectural design and the like. The present invention relates to a polyhedron shape input display device suitable for inputting a polyhedron shape.

[Prior Art] Conventionally, in order to define a polyhedron shape on a computer, a method of mainly inputting the three-dimensional coordinates of a group of vertices by a numerical value, and inputting a plurality of projection views (for example, a front view and a plan view) in two-dimensional coordinates Although there is a method of inputting with a device (digitizer) and generating corresponding three-dimensional data by inputting corresponding points of a plurality of drawings, the former method of inputting numerical values is apt to cause an order of magnitude error, while The latter method of inputting from a plurality of projection views has a problem that an error is likely to occur at the stage of associating vertices between a plurality of drawings.

[Problems to be Solved by the Invention] In the present invention, when the three-dimensional data of a polyhedron shape is input to a computer or the like, the above method, which is apt to make an error for human beings, is revised, and the same operation as drawing a figure is performed. An object of the present invention is to provide a polyhedron shape input display device capable of inputting.

[Means for Solving the Problems] A polyhedral shape input display device of the present invention for solving the above problems is connected to a two-dimensional coordinate input device for inputting a projected shape of a polyhedron and the two-dimensional coordinate input device. An arithmetic processing device, and a display device for displaying the polyhedral shape in a state of being projected in a specific direction based on the output of the arithmetic processing device,
In a polyhedron shape input display device including a line-of-sight direction input device for giving the projection direction, the arithmetic processing device is connected to the two-dimensional coordinate input device, and ridge line information about the input polyhedron shape is output. Based on the input information processing unit, the output of the input information processing unit, and the shape data that has already been input, when the ridge line information is input in face units, the new face becomes a face that has already been three-dimensionally converted. A backprojection determination unit that determines the number of ridgelines in contact with each other, and a backprojection data processing unit that calculates the inclination of a newly input surface by the three-dimensional conversion process based on the output of the backprojection determination unit A polyhedron shape data storage unit that stores the polyhedron shape data, and a projection transformation unit that converts the coordinates of the polyhedron shape data into the direction designated by the line-of-sight direction input device and outputs the data to the display device. It is characterized in that it has assumed that a part.

[Operation] According to the polyhedron shape input / display device of the present invention having the above-mentioned configuration, the polyhedron shape is input by substantially the same operation as drawing a figure from the two-dimensional coordinate input device, and the line-of-sight direction input device is used to input the line of sight. By designating the direction, the desired polyhedral two-dimensional projection figure can be displayed on the display device based on the output of the arithmetic processing device.

The mode of processing in the arithmetic processing device will be specifically described. In the arithmetic processing in this device, information is added by introducing a restriction condition that does not make the operator feel unnatural and a constraint condition for the surface related to the polyhedron. Then, the two-dimensional shape data is converted into three-dimensional data. Therefore, first, in the two-dimensional coordinate input device, the projection display surface of the polyhedron shape is identified with the two-dimensional shape input surface, the ridgeline of the polyhedron shape to be projected is input, and the backprojection determination unit The degree of freedom for backprojection is determined based on the ridge line information about the polyhedron shape output from the input information processing unit and the shape data that has already been input. As a result, the basic restriction conditions set in advance are set. Below, information of a new surface in the three-dimensional space to be backprojected is obtained from the two-dimensional coordinates.

The limiting condition can be set as follows, for example.

1. The projection is not a perspective projection but an orthographic projection (parallel perspective).

2. Enter the ridgeline that forms the face in face units. That is, it is assumed that after inputting one ridgeline of a surface, all ridgelines in the surface can be input before inputting the ridgeline of another surface.

3. Input from adjacent faces in order. That is, when one face is input, three-dimensional conversion is performed on a face-by-face basis, so when inputting the next adjacent face, the information of the ridge line in contact with the face that has already been input is used, and Reduce the degree of freedom.

Under these restriction conditions, the backprojection data processing unit performs three-dimensional conversion processing on the inclination of the surface backprojected in the orthogonal projection direction in the following three cases.

1. When there is no 3D transformed surface The input surface is parallel to the projection surface (which matches the input surface) in 3D space. The reason is that the projected area is the maximum (the back projected area is the minimum), the shape matches the actual surface shape, and there is no projection distortion, so that the operator feels it naturally. Therefore, the input first surface is back-projected onto a plane (back-projection surface) in the space with the distance from the viewpoint as a certain default value, and the position and inclination are fixed.

2. When there is one ridge line that is already connected to the surface that has been three-dimensionally converted. The ridge lines that compose the input surface are three-dimensionally converted and are displayed again on the projection surface. The ridge lines projected and displayed after being three-dimensionally converted are apparently coincident with each other. Therefore, when a new surface adjacent to the surface that has already been three-dimensionally converted is input,
Since one ridge line has already been three-dimensionally converted, this becomes a new constraint condition, and is three-dimensionally converted into a surface having an inclination that maximizes the projected area under the condition. Again, the projector feels natural because of the direction in which the projected area is maximized.

3. When there are multiple ridgelines that are already connected to the 3D-converted surface, the multiple ridgelines have three-dimensional coordinates, so if these ridgelines are on the same plane, those ridgelines are Since the newly input plane should exist in the same plane, the inclination of the backprojected plane can be easily obtained.

Information is added by using the above conditions, and the ridge line data of a three-dimensional polyhedron that cannot be uniquely determined in principle,
It becomes possible to generate from the ridge line group on the two-dimensional projection plane.

[Examples] Examples of the present invention will be described in detail below with reference to the drawings.

As shown in FIG. 1, a polyhedron shape input / display device according to the present invention is a tablet or the like for inputting two-dimensional coordinates of each part of a polyhedron shape to be input by designating a position on an input surface 2.
Dimensional coordinate input device 1 and arithmetic processing device 3 described in detail below
And a display device 4 for two-dimensionally displaying on the screen the orthographic projection of the polyhedron shape in the three-dimensional space in a specific direction based on the output of the arithmetic processing device 3, and for displaying on the display device 4. It is mainly composed of a line-of-sight direction input device 5 provided with a series of dials or keys for inputting a direction for performing the orthographic projection.

As the arithmetic processing unit 3, a circuit for obtaining a two-dimensional figure when the shape data of the polyhedron in the three-dimensional space is orthographically projected in a specific direction, and the input two-dimensional figure is inversely projected back into the three-dimensional space. A conversion circuit is needed.

Moreover, since information is insufficient when back-projecting from a two-dimensional figure, the conditions relating to the above-described input procedure are set in advance, and the inclination of the projection area is maximized in the allowed degrees of freedom. A condition of three-dimensional conversion is added to the surface. Then, by inputting a ridge line group that constitutes one surface at a time, the one surface is input, and when one surface is completely input, the surface is immediately back-projected to the three-dimensional space and Find the equation in dimensional space.

If this is obtained, the equation of the surface in the three-dimensional space becomes known, so that all the points in the surface can be converted from the two-dimensional coordinates on the projection surface into the three-dimensional coordinates without ambiguity. Three
After being converted into three-dimensional coordinates, the next input surface is a surface adjacent to the surface converted into three-dimensional coordinates. The reason is,
A ridge line common to these two faces (called a common ridge line)
Is already converted into three-dimensional coordinates, and this surface can be used as a clue to convert this surface into three-dimensional coordinates.

Therefore, among these processes, how to back-project onto a surface in the three-dimensional space when one surface is completely input becomes a problem. Here, consider three cases. .

If there is a surface adjacent to the surface you are trying to input, that surface must have already been converted into three-dimensional coordinates. Therefore, the ridge line at the boundary between this adjacent surface and the surface you want to input is on both surfaces. It becomes common and common ridgeline. If the face you are trying to enter does not contain a common edge, and if it contains only one,
And a case where a plurality of lines are included is determined based on three cases, and different conversion processing is performed.

First, when there is no common edge line, the first input surface does not have any three-dimensional information, so the equation is calculated as a surface parallel to the projection surface. At this time, although the equation varies depending on the size of the distance from the line-of-sight position, three-dimensional conversion is performed using a predetermined distance. Next, when there is one common edge line, a three-dimensional coordinate is obtained by further setting a restriction that the area is the minimum when backprojected under the constraint. Finally, when there are a plurality of common edges, if they are on the same plane in the three-dimensional space, the newly input surface coincides with this same plane, so that the three-dimensional coordinates can be easily obtained.

As described above, when backprojecting from a two-dimensional figure, since information is insufficient, the above-mentioned constraint is added according to the current data, for example, the number of common edges described above, and data processing is performed. .

Therefore, as shown in FIG. 1, the arithmetic processing device 3 includes an input information processing unit connected to the two-dimensional coordinate input device 1, specifically, a tablet processing circuit connected to a tablet and its input processing unit. Based on the output and the shape data previously input, it is determined whether the closed area can be input on the projection surface, and when the closed area can be input, that is, at the stage where a new surface to be backprojected is formed, A projection determination unit (backprojection determination circuit) that determines the number of common edges whose new surface is already in contact with the three-dimensionally converted surface, and a three-dimensional conversion process based on output information from this backprojection determination unit. A backprojection data processing unit (backprojection data processing circuit) that calculates the inclination of a newly input surface, a polyhedral shape data storage unit (polyhedral shape data storage device) that stores the input polyhedral shape data, and a polyhedral shape And a projection transformation unit and outputting the coordinate conversion on the display device 4 in the specified direction (projection conversion circuit) by line-of-sight direction input device 5 data.

The configuration and operation of the arithmetic processing device 3 will be described more specifically with reference to FIGS. 2A to 2C. First, in the tablet processing circuit connected to the tablet, the plane of the input surface 2 is the xy plane. Then, the edge information about the input polyhedron shape, that is, the pair of coordinates of both end points of the edge is temporarily stored in the memory, and the tablet processing circuit outputs the input line segment start point and end point two points. Two two-dimensional coordinate values (x ₁ , y ₁ ) and (x ₂ , y ₂ ) are output as digital signals.

The ridge line having this two-dimensional coordinate value is displayed on the display device 4 as it is, and at the same time, this ridge line information is input to the next backprojection determination circuit.

The logical relationship between the tablet and the display device 4 will be described. First, the tablet is a device capable of inputting two-dimensional coordinates from the position information of the planar movement of the operator's hand, and the coordinate input surface 2 is a logical device. Generally corresponds to the screen of the display device 4. That is, the movement of the hand is reflected as a cursor on the screen so that the input position can be visually confirmed. The input surface 2 of this tablet is further made to coincide with the display surface of the display device 4 as a two-dimensional projection surface having a polyhedral shape. Therefore, the plane on which the operator inputs the two-dimensional coordinates corresponds to the plane on which the polyhedral shape is projected, and the projection direction is designated by the line-of-sight direction input device 5.

The back projection determination circuit always refers to the already input data. There are two types of data that have already been input: two-dimensional ridge line data on the input surface 2 and ridge line data that has already been converted into three-dimensional coordinates as surface data. The two-dimensional ridge line data on the input surface 2 alone or the ridge line data obtained by projecting the three-dimensionally converted ridge line data on the two-dimensional input surface 2 together creates a new closing on the input surface 2. When the area is formed, it is regarded as one surface and the number of common edges is determined. The backprojection data processing circuit performs a three-dimensional conversion process on the inclination of the new surface backprojected in the orthogonal projection direction based on the output information of the backprojection determination circuit. In this case, the backprojection data processing circuit performs the conversion processing in the above three cases according to the number of common edges.

A typical example of these three cases is shown in FIGS.
Is. FIG. 2A shows a case where there is no common edge line, that is, a case where the first surface is input. Specifically, the ridge line group 11 input to the input surface 2 and the ridge line group already input form a closed region (referred to as a closed region), but when there is no common ridge line, the closed region is Back projection plane in three-dimensional space
It is assumed that the surface 13 on the surface 10 is projected on the input surface 2 which is also the projection surface. At this time, there are infinite ways to select the surface 10, but here, as an example, the most natural assumption is introduced to determine the surface 10. The assumption is that the surface 10 is parallel to the input surface 2 and is apart from the input surface 2 by a predetermined distance.

After being converted into the surface 13 in the three-dimensional space under such an assumption, the data is sent to the polyhedral shape data storage device in the arithmetic processing unit 3 of FIG. 1, and the surface 13 is transferred to the input surface 2 by the projection conversion circuit. When projected and displayed, this matches the first input surface. Therefore, although the operator should have input on the input surface 2, the operator has input on the surface 10 in the three-dimensional space. Therefore, if the projection direction is changed by the line-of-sight direction input device 5 (this apparently rotates the three-dimensional space), the input surface 10 can be seen from an oblique direction. This is shown in FIG. 3B.

A of FIG. 3 shows the hexagonal surface that is input first, and also shows the coordinate axes O-XYZ in the three-dimensional space for the sake of easy understanding. After inputting the hexagon in FIG. 3A (immediately converted to three-dimensional coordinates and the hexagon is displayed as the projection), the line-of-sight direction (also the projection direction)
The screen after the change is shown in FIG. 3B. This shows that the input hexagon can be seen from another direction with the coordinate axes fixed in the three-dimensional space. Thus, if there is no previously input surface, the surface parallel to the input surface 2
The closed region entered as 13 is transformed.

Next, a description will be given of the processing when there is one common edge line, in the case where there is a closed area that was previously input and converted into three-dimensional coordinates, and a new surface is input adjacent to it. Moreover, this is the case where there is only one common ridgeline with the closed region. Since the end points of this common edge line are points on the closed region that have already been converted to surfaces in the three-dimensional space, they have been converted to have three-dimensional coordinate values, and are further projected onto a two-dimensional plane by projection conversion. Is displayed on the display device 4.

In this case, if the end points of the ridge line of the newly input surface match the end points of the ridge line that have already been input on the projection plane, they are 3
It has the same coordinate values in the dimensional space. And
When a closed region is formed by the newly input ridge line and the already input ridge line, the region is regarded as a closed plane region even in the three-dimensional space. At this time, if the inclination of the surface formed by the closed region in the three-dimensional space is known, it can be calculated from the two-dimensional coordinate value by three.
The coordinate value of the dimensional space is uniquely determined.

Regarding specific processing when there is one common edge line,
This will be described with reference to FIG. 2B. From the state of FIG. 2A, the direction of orthogonal projection is changed by using the line-of-sight direction input device 5 such as a dial, and the second surface 14 is input from the coordinate input device 1.
At this time, as shown in FIG. 2B, if one ridge line 16 of the first surface 13a input to the XYZ coordinate system is shared with the second input surfaces 15a to 15c, the second surface 14a When back-projecting, the degree of freedom decreases to 1. That is, the newly input second surfaces 15a to 15c can have any inclination including the shared ridge line 16, and thus have one degree of freedom. Therefore, in this case, the second surface 14 is uniquely determined as a surface having a specific orientation by adding a constraint condition that the area is set to a direction in which the back projection is minimized. It will be. In addition,
13b shows a state in which the input surface 13a is projected on the input surface 2 and displayed as a line segment.

According to a mathematical expression, when the line-of-sight vector is ν in the three-dimensional space, the common ridge direction vector is e, and the inclination of the input surface to be newly set is n, n = ± e × (e × υ ). However, the compound number shall be either one so that n · υ <0.

When there are a plurality of common edges, two or more previously defined surfaces 17 and 18 exist as adjacent surfaces, as shown in FIG. 2C, so that the inclination of the surface is shared by the adjacent surfaces. It is easily determined as the surface 20 including the common ridgelines 21 and 22 of.

As is clear from the above description, if there is no common ridge, the backprojection data processing circuit three-dimensionally transforms the closed area as a surface having the same inclination as the input surface. When the number of common ridges is one, three-dimensional conversion is performed as a surface having an inclination that minimizes the area when backprojected in the plane including the common ridge in the three-dimensional space. When there are multiple common edges, it is determined whether or not they are on the same plane in the three-dimensional space, and if they are on the same plane, the inclination of that surface is output. Above, it is determined that the closed region is not on the same plane in the three-dimensional space.

To summarize the function of the backprojection data processing circuit, the inclination and position of the plane in the three-dimensional space to be backprojected are obtained with reference to the common ridgeline, and the input plane (= projection plane) is derived from the plane.
Since the ridge line group when projected on is given as the input ridge line group, on the contrary, the input ridge line group can be back projected onto the designated plane in the three-dimensional space.

The calculation of this part can be expressed more accurately by mathematical expressions as follows.

First, the spatial coordinate system fixed in the three-dimensional space is O-XYZ.
And the visual coordinate system fixed in the projection plane (xy plane coincides with the screen) is o-xyz. The output of the backprojection judgment circuit is a three-dimensional plane equation in the spatial coordinate system of the closed area, AX + BY + CZ + D = 0 (however, A ² + B ² + C ² = 1) ・ ・
(1) and two-dimensional coordinate value group (xi, y
i) (where i = 1, 2, ...). Spatial coordinate system OX
In YZ, the plane and one point (X, Y,
The Z), a representation in visual coordinate system o-xyz, respectively, ax + by + cz + d = 0 ( ^{where, a 2 + b 2 + c} 2 = 1) ··
Assuming (2) and (x, y, z), the mutual relationship is expressed by the equations (3) and (4) using the 4 × 4 conversion matrix M.

(X, y, z, 1) = (X, Y, Z, 1) M .. (3) (a, b, c, d) = (A, B, C, D) (M- ¹ ) ^T .. (4) In the backprojection data processing circuit, the two-dimensional projection position (x
i, yi) (where i = 1, 2), the transformation matrix M and the coefficients A, B, C, D of the plane equation are known, the processing for obtaining the values of X, Y, Z is performed. This is obtained from the equation (2), but in the equation z = (ax + by + d) / (− c) ··· (5), since a, b, c, d are obtained from the equation (4), z
Is determined. Then, X, Y, and Z can be obtained from the value of z and the expression (3). Therefore, the output of this circuit represents the end point of the input line segment by the coordinate value of the spatial coordinate system (Xi, Yi, Zi)
(Where i = 1, 2, ...).

In this way, the surfaces of the object to be input are drawn on the input surface 2 of the coordinate input device 1 one by one, and these surfaces are sequentially defined. At the stage when all the surfaces are defined, the shape data of Input will be completed.

The polyhedron shape data storage device takes in the ridge line data converted into three-dimensional coordinates, and refers to the ridge line data which is already existing polyhedron shape data, while referring to mutual connection information (which ridge line is connected to which ridge line, Topological information such as which is which ridge line constitutes the number of faces) is added and stored.

Furthermore, the 3 data stored in this polyhedron shape data storage device are stored.
The dimensional data is sent to the projection conversion circuit. This projection conversion circuit is a circuit that performs standard graphics projection conversion, and performs a series of data conversion such as scaling conversion, rotation conversion, movement conversion, and window conversion by matrix calculation, and from the three-dimensional ridge line data to the display device 4. It is a processing circuit for obtaining two-dimensional coordinates to be displayed above. That is, conversion is performed such as from which direction the three-dimensional data is viewed, or how much the three-dimensional data is viewed from the viewpoint of scaling or movement. While looking at the drawing projected on the display device 4 in real time, it is possible to see from which direction (the direction in which the projected shape is displayed on the display device), how much to enlarge or reduce, etc. The device for changing the line-of-sight direction input device 5. Based on the line-of-sight direction data sent from the line-of-sight direction input device 5 and the data such as the enlargement / reduction ratio, the data obtained from the polyhedron shape data storage device is subjected to a conversion operation, and the two-dimensional coordinate values of the converted ridge line group are displayed. It is sent to the device 4 and displayed.

3A to 3H exemplify a state in which each stage of the definition of the hexagonal prism according to the present invention is displayed on the screen of the display device 4.

FIG. 3A shows a state in which a hexagon is input as a closed area on the initial screen showing the coordinate axes of the spatial coordinate system. When this input is made, the plane equation is immediately determined to be parallel to the XY plane, and the ridge line is backprojected in the three-dimensional space. Therefore, in the state of FIG. 9B in which the spatial coordinate system is rotated, the hexagon can be seen from another direction. further,
FIG. 6C shows a state in which the spatial coordinate system is rotated and three ridge lines are newly input in a state where the hexagon is rotated until it becomes almost a straight line, and a region adjacent to the hexagon is defined. At this time, since one of the ridge lines forming the newly defined quadrilateral region forms a common ridge line with the hexagon that has already been converted into the three-dimensional space, the plane equation of the quadrilateral region is ,
It is determined to include this common edge line. After that, the spatial coordinate system is further rotated obliquely to define the third region, which is shown in FIG. In this case, among the four edges that form the newly defined closed area, there are two common edges that have already been transformed into the three-dimensional space, so the plane equation of the new closed area is uniquely determined. . 3E, F, G, and H also show a state in which the spatial coordinate system is set in the directions shown in the figure and the ridge lines are successively input. From the same figure D to the same figure H, although the spatial coordinate system is fixed in the same direction, the input ridge lines are back-projected in different three-dimensional spaces and the correct polyhedron shape can be defined. have.

As described above, according to the polyhedron shape input display device, it is possible to visually draw the polyhedron shape on the input surface of the coordinate input device and generate the three-dimensional data thereof.

In addition, when drawing a figure on the input surface of the two-dimensional coordinate input device, for example, a method of inputting an accurate value of the length is performed by rounding inside the arithmetic processing device or by inputting a separate numerical value and displaying it. Can also be used together.

Further, the arithmetic processing device for performing the condition setting, the surface inclination setting, the projection conversion, and the like described above can be realized as a hardware circuit or a software program in a computer.

[Effects of the Invention] As is clear from the above-mentioned detailed description, according to the polyhedral shape input display device of the present invention, the polyhedral shape can be input by the same operation as drawing a figure, resulting in an erroneous input. Can be very small.

[Brief description of drawings]

FIG. 1 is a block diagram of a polyhedron shape input / display device according to the present invention, FIGS. 2A to 2C are explanatory diagrams of its operation, and FIGS.
H is an explanatory view showing a mode of definition of a hexagonal prism by the above device. 1 ... Two-dimensional coordinate input device, 2 ... Input surface, 3 ... Arithmetic processing device, 4 ... Display device, 5 ... Line-of-sight direction input device.

 ─────────────────────────────────────────────────── ─── Continuation of the front page (72) Yoshiki Kishi Inventor Yoshiki Kishi 1-4-1, Yatabe-cho, Tsukuba-gun, Ibaraki Inside Institute for Product Science, Institute of Industrial Science and Technology (56) Reference JP-A-58-195977 (JP, A) Kaisho 58-24956 (JP, A)

Claims (1)

[Claims] 1. A two-dimensional coordinate input device for inputting a projected shape of a polyhedron, an arithmetic processing device connected to the two-dimensional coordinate input device, and a specific direction of the polyhedral shape based on an output of the arithmetic processing device. In a polyhedron shape input display device including a display device for displaying in a state of being projected on a screen, and a line-of-sight direction input device for giving the projection direction, the arithmetic processing device is connected to the two-dimensional coordinate input device, Based on the input information processing unit that outputs the ridge line information about the input polyhedron shape, and the output of the input information processing unit and the shape data that has already been input, at the stage where the ridge line information is input for each face, the new A back-projection determination unit that determines the number of ridge lines that are in contact with a surface that has already been three-dimensionally converted, and based on the output of the back-projection determination unit, a new input is performed by the three-dimensional conversion processing. The backprojection data processing unit that calculates the tilt of the applied surface, the polyhedral shape data storage unit that stores the input polyhedron shape data, and the coordinate conversion of the polyhedron shape data to the direction specified by the line-of-sight direction input device. A polyhedron shape input display device, comprising: a projection conversion unit for outputting to a display device.